No magic exists in this setting beyond what is explicitly described in this quesiton. The setting is vaguely European medieval. The question centers around a town large enough to support a nobleman complete with his keep. The town and the immediate surrounding area have a variety of industries, most notably farming, logging, mining (iron ores), and a variety of local craftsmen.

A carpenter one day discovered that if he built a water wheel and mounted it horizontal it would turn, building up speed. Eventually it would reach somewhat more momentum than an aggressive stream would produce. A smaller water wheel with smaller paddles produces less force, and poorly constructed water wheels will eventually break as though actually being pressed on by a force of water. In fact, for nearly all intents and purposes, the wheels act like they are being pushed by an invisible stream of water.

What exactly constitutes a "water wheel" isn't clear, but if through experimentation the townsfolk determine that any wheel that looks like a water wheel and was intentionally crafted in the style of one seems to possess this effect. The less horizontal the wheel is, the less the effect is present. The further the wheel is away from the town, the less the effect is (at about 50 miles out from town the effect is entirely gone).

Effectively this creates a means of getting mechanical power like water generated power of that time, but be largely unburdened where one is getting the power (no need to be near a stream).

What effects would this new energy source have on local industry in the relative short term (<30 years)?

$\begingroup$@Bellerophon Amusing, but this idea is largely a modern myth. You'd be hard pressed to find cases of people in the Middle Ages being accused of witchcraft or hailed as miracle workers because they came up with a new invention. Bear in mind that many scientists and inventors of the era were priests, monks, or professors at universities run by the church.$\endgroup$
– JayMay 12 '17 at 18:00

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$\begingroup$@Jay True. of course, if they managed to invent something that runs on magic...$\endgroup$
– BellerophonMay 12 '17 at 18:06

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$\begingroup$To those voting "Too Broad," could you please review what scope within "local industry" would make it sufficiently narrow?$\endgroup$
– Nex TerrenMay 12 '17 at 18:14

3 Answers
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Water wheels were one of the major turning points fro humanity in moving towards machine rather than animal labour. They were used in corn/grain mills primarily but were also available for sawmills, fulling mills (cleaning and preparing cloth) and many others.

The first big advance I can think of for your town is breadth of industry. At the minute labour intensive industries such as milling corn have to be done by hand or on the (presumably limited) river bank. With the area these activities can be done in increased dramatically there will be room for more mills widening the industrial scope to include all major watermills of the period. In your area sawmills and iron trip hammers will probably be particularly popular due to the logging and mining industries.

People are inventive (evidence here) so it won't be long before waterwheels become more used in your town. One new technologies I can thing of are cranes. In your time period most heavy lifting was done by humans walking inside a giant wheel which wound a rope. Using waterwheels to turn the ropes will greatly expand your lifting capacity. Some Islamic water wheels could lift 2550 litres of water a minute so that suggests some pretty hefty lifting strength. I don't know exactly how much these water wheels can lift which should make lifting iron ore from mines easier as well potentially providing winches for tree extraction. The only issue might be getting the stuff off the waterwheel at the top if you can't stop it turning but that issue should be resolvable with some sort of brake or coupling/uncoupling axle. The crane would also obviously be useful for building stuff. See Guedalon castle, France for an example of the classic medieval hamster wheel cranes in action.

A slightly less likely technology would be the first cars. If a waterwheel were attached to a (larger) normal wheel then you would have a self propelling car. Whether these would replace carts I don't know as I suspect their would be a lot of issues with building them but it is definitely a possible technology.

I suspect I have missed a lot of potential applications such as military applications (not really useful in a small town) and other civil ones.

It quickly becomes a large city

This sort of concentrated mechanical power happened in Roman times. There are at least two known concentrations of water-powered mills at Barbegal in southern France, and Janiculum outside of Rome. Another may have been at Amida (modern Diyarbakir) in Turkey.

Barbegal was likely the more powerful of the two installations. The Romans built a long aqueduct from the Alpilles hills to Arles, a city of maybe 50,000 at the time. The aqueduct was designed with a steep drop down a hillside; at this drop a complex of 16 overshot mill wheels was installed. The mill complex could produce something like 4.5 tons of ground flour per day.

Janiculum, was the same thing, except for Rome. During the time of Aurelian, (at least) one of the aqueducts was redirected to run staight down the side of Janiculum hill, previously on the outskirts of town. The Aurelian walls of Rome were then extended out to protect the mills and the town's bread supply. The mills were still in use as late as the time of Pope Gregory IV (-844).

The fact that both these large industrial industrial installations were used exclusively for grain milling shows the scale of grain milling in the ancient (and medieval) world. If a person needs a 1-2 lb of flour a day, then a city of 1 million like Rome needs 500 to 1000 tons of grain milled per day. Obviously, this analysis only applies if your people's staple food is wheat or corn or cassava or something that needs milling. If their staples are rice or potatoes, this argument isn't valid.

The biggest relative advantage for a city with free magic power is in milling grain. Logs and stone and other things are heavy and expensive to move; even if you can make them cheaper with mills in this town, most of the cost of getting these items to customers are transportation costs, with medieval technology. Grain, however, has to come to a city in grain form anyways (flour spoils faster and can't get wet). So for any given city size, you get mostly free grain milling with no extra transportation costs with these magic mills.

Therefore, I conclude that the biggest advantage of this city will be cheap food, which will make craftsmen and people of all sorts want to move there. Many of these crafts can't be aided by mills anyways (leather, goldsmithing, dyeing).

As other answers have mentioned, you'd get an accumulation of lots of industry that would otherwise be found only on large rivers. I think the biggest gamechanger, though, is that the magic wheels are portable; you can set them up anywhere, move them from place to place, even have them power their own transport! Automobiles might be too big a bar to clear, but other means of transport would certainly be enabled, from trains on railways to paddlewheelers on canals. If the effect goes out dozens of miles, that binds the entire region (and its various manufactories) together into a medieval metropolitan region.